Can't use displacement modifier to create low poly water
The "new texture" is still on the defaults, which just aren't very interesting, yet. It just has too little noise to do anything on the displacement.

Click on the button all the way to the right of the texture's name in the displacement modifier. This will take you to the settings for this texture. You'll need to reduce the scale of the texture so that the portion mapped to the plane has some variation, instead of being mostly the same color.

EDIT: Or Zak might be right, there might just not be an actual texture associated with it, yet.